On the applicability of the Cauchy-Born rule

Numerical computations are presented confirming the possible breakdown of the Cauchy-Born rule for an infinite planar square lattice whose vertices are occupied by interacting particles, in agreement with the theoretical predictions of Friesecke and Theil (2002). Energy minimization yields solution branches exhibiting a non-zero deviatoric inner displacement for shearing and extensional deformation. A statically square lattice can become unstable when subjected to sufficiently large deformation. Numerical solutions of a boundary-value problem illustrate the development of irregular lattice configurations under supercritical conditions.